Method for measurement of the shape and curvature of a cornea

ABSTRACT

A METHOD AND APPARATUS ARE PROVIDED FO MEASURING THE APICAL RADIUS OF CURVATURE AND ECCENTRICITY OF A CONICOID SURFACE, SUCH AS A CORNEA OR LENS, BY SUPPORTING LARGER AND SMALLER CIRCULAR TARGETS CONCENTRIC TO THE OPTICAL AXIS OF A ELESCOPE WHICH HAS ITS OPTICAL AXIS ALIGNED WITH THE OPTICAL AXIS OF THE CONICOID SURFACE. THE TELESCOPE IS FOCUSED ON THE REFLECTED IMAGE OF THE SMALLER TARGET WHICH IS MEASURED TO DETERMINE THE APICAL RADIUS OF CURVATURE OF THE CONICOID SURFACE. THE TELESCOPE IS THEN FOCUSED ON THE REFLECTED IMAGE OF THE LARGER TARGET WHICH IS MEASURED, AND ITS SIZE AND THE DETERMINED APICAL RADIUS OF CURVATURE ARE USED TO DETERMINE THE ECCENTRICITY OF THE CONICOID SURFACE.

Sept. 5, 1972 D. VOLK Re. 27,475

METHOD FOR MEASUREMENT OF THE SHAPE AND CURV'ATURE OF A CORNEA OriginalFiled Mai-ch 5, 1968 I 4 Sheets-Sheet 1 INVENT OR. Dav/0 VULK Sept. 5,1972 VQLK Re. 27,475

METHOD FOR MEASUREMENT 01" IIII'I SllAl'l'i AND CUHVA'IURE 01 A CORNEAOriginal Filed March 5, 1968 4 Sheets-Sheet 3 jig/L C I INVENTOR.

.DflV/D VOL/f wagf wsiy D. VOLK Sept. 7 5, 1972 METHOD FOR MEASUREMENTOF THE SHAPE AND CURVATURE OF A CORNEA Driginal Filed March 5, 1968 4Sheets-Sheet 3 I NVENTOR. Dav/n VOLK 7TORNEYJ D. VOLK METHOD FORMEASUREMENT OF THE SHAPE AND CURVATURE OF A CORNER Original Filed March5, 1968 4 Sheets-Sheet 4.

United States Patent Oifice Re. 27,475 Reissued Sept. 5, 1972 27,475METHOD FOR MEASUREMENT OF THE SHAPE AND CURVATURE OF A CORNEA DavidVolk, 2460 Fair-mount Blvd., Cleveland, Ohio 44106 Original No.3,542,458, dated Nov. 24, 1970, Ser. No. 710,557, Mar. 5, 1968.Application for reissue Feb. 8, 1971, Ser. No. 113,775

Int. Cl. A61b 3/00, 3/10 US. Cl. 351-39 1 Claim Matter enclosed in heavybrackets I: appears in the original patent but forms no part of thisreissue specification; matter printed in italics indicates the additionsmade by reissue.

ABSTRACT OF THE DISCLOSURE A method and apparatus are provided formeasuring the apical radius of curvature and eccentricity of a conicoidsurface, such as a cornea or lens, by supporting larger and smallercircular targets concentric to the optical axis of a telescope which hasits optical axis aligned with the optical axis of the conicoid surface.The telescope is focused on the reflected image of the smaller targetwhich is measured to determine the apical radius of curvature of theconicoid surface. The telescope is then focused on the reflected imageof the larger target which is measured, and its size and the determinedapical radius of curvature are used to determine the eccentricity of theconicoid surface.

This invention relates to a method and apparatus for determiningsimultaneously the apical radius of curvature of the cornea and theshape of the cornea in terms of the eccentricity of conicoids ofrevolution which approximate the shape of the cornea. The same methodand apparatus can be used for the determination of apical radius ofcurvature and eccentricity of conicoids of revolution used for both theanterior and posterior surfaces of contact lenses. The method andapparatus is also applicable to similar determinations on the muchlarger conicoids of revolution used for spectacle lenses and for moldsfor the casting of such lenses.

In the drawings:

FIG. 1, not drawn to scale, is a diagrammatic representation of thepositions of points, surfaces and chief rays involved in image formationby reflection from a spherical surface of an off-axis object point;

FIG. 2, not drawn to scale, is a diagrammatic representation of thepositions of points, surfaces and chief rays involved in image formationby reflection from a conicoid of revolution of an off-axis point;

FIG. 3, drawn to scale, is a diagram comparing the spherical image ofFIG. 1, to the right of the central axis, with the conicoid orparaboloid image of FIG. 2, to the left of the central axis;

FIG. 4 is a side elevational view, partly in section, of apparatussuitable for carrying out the method of this invention; while FIG. 5 isan enlarged View of reticle 33 with usual cross lines.

When the cornea is not a surface of revolution but has two principalmeridians, the same method and apparatus can be used for thedetermination of the apical radius of curvature and eccentricity in eachof the principal meridians. Hereafter the description will apply to thecornea in terms of conicoids of revolution and I will speak of theapical radius of curvature and eccentricity of the cornea. It is to beunderstood that when the cornea has principal meridians, each principalmeridian can be considered in terms of the apical radius of curvatureand eccentricity of the approximating conic section. 7

It is known that the anterior surface of the cornea is most highlycurved at its apex, and from said apex to the periphery it decreasescontinuously and regularly in curvature, resembling prolate ellipsoids,paraboloids, or byperboloids. The rate of decrease in meridional andtransmeridional curvatures for corneas of a given apical radius ofcurvature varies from cornea to cornea, depending upon the eccentricityof the cornea.

When the corneal surface is used as a mirror, the size of the cornealimage of a relatively large target of a given size and for a givenobject distance will vary according to the two variables which define aconicoid of revolution: apical radius of curvature and eccentricity.

For corneas of a given apical radius of curvature, the size of the imageof a given size target centered about a common optical axis of thecornea and of the telescope, perpendicular to the optical axis of thetelescope and at a given distance from the apex of the cornea, saidimage observed through the telescope from a point along the axis of thecornea, will increase as the eccentricity of the cornea increases. Thusa basis is established for determining the eccentricity of a givencornea in terms of the size of the corneal image of a given target.

When the apical radius of curvature of the cornea is determined byophthalmometry, the target is relatively 'small, so that the portions ofthe cornea involved in the formation of the observed corneal image arequite close to the apex of the cornea. When this is the case, the radiusof curvature determined is substantially independent of the eccentricityof the cornea, since the rates of change in curvature about the apex ofa cornea or conicoid are so small that the radius of curvaturedetermined with a relatively small ophthalmometer target issubstantially that of the spherical surface which osculates the corneaor conicoid at its apex.

However, when a relatively large target is used, the portions of thecornea involved in the formation of the observed corneal image are atrelatively great distances from the corneal apex. For corneas of a givenapical radius of curvature but differing eccentricities, and a givenrelatively large size target at a given target distance, the greater theeccentricity, the more distant from the corneal apex are the portions ofthe cornea involved in the formation of the observed corneal image, andthe larger is the observed corneal image.

Hence in the method of this invention, it is first necessary todetermine the radius of curvature of the corneal apex to establish themagnitude of the surface measured, as distinguished from itseccentricity. This is achieved by ophthalmometry, using a small targeton the ophthalmometer, measuring the size of the corneal image of thetarget and applying the mirror equations for paraxial conditions, to thedata obtained. These equations are: (1) the object size-image size ratioequation.

y'/y=u'/u (1) where y is the size of the image, y is the size of thetarget, u is the object distance, and u is the image distance. y, theimage size, is measured with the opthalmometer, and said size is appliedto the above equation to determine the image distance u. Once the imagedistance is determined, it is applied to the second mirror equation (2)relating the conjugate foci and the radius of curvature of the mirrorsurface:

1/u+1/u'=2/r (2) to determine the apical radius of curvature, r, of thecore cornea.

Having determined the apical radius of curvature of the cornea, themethod and apparatus are then used to produce a relatively large cornealimage of a relatively large target of a given size, the object and imagebeing symmetrical with respect to the common optical axis of he corneaand telescope of the ophthalmometer, and to measure the size of saidcorneal image. The image, for a. cornea of a given apical radius ofcurvature, varies in size as a function of the eccentricity of thecornea, so :hat measured image size can be used to indicate the:ccentricity of the cornea. The techniques for measurement of the sizeof the corneal images are well known in the art of corneal measurementand need not be described herein. These involve the method of doublingthe image, or the direct measurement of the size of the image by meansof a calibrated reticle in the eyepiece of the telescope of theophthalmometer, or the telescope image may be matched in size by asuperimposed image of tdjustable size, the size of the superimposedimage indi- :ating the size of the corneal image.

Conventional ophthalmometry utilizes a relatively small target, and theparaxial mirror equations (1) and (2) are applicable. However, if alarge target is used on the ophthalmometer, the mirror equations must bemodifled to take into account the significant obliquity of the incidentand reflected light rays with respect to the corneal surface.Furthermore, the peripheral corneal surface Is astigmatic, havingmeridional and transmeridional principal directions and principalcurvatures which vary along a meridian. The observed image of aperipheral target point will be astigmatic with the focal lines beingmeridional and transmeridional in direction. If a circle centered aboutthe common optical axis of the cornea and telescope is used as thetarget, or if a series of point objects arrayed closely on said circleis the target, overlapping of the transmeridional focal lines of allpoints on said circle produces a sharp circular image whose size can bemeasured.

The modified mirror equation for said circular image, for non paraxialconditions, where the angle of incidence is oblique with respect to thereflecting surface is:

where i is the angle of incidence of the chief ray from a point on saidcircular target with respect to the reflecting surface, u is the imagedistance of the transmeridional focal line, projected back along thereflected chief ray, from the point of reflection of said ray, and r isthe meridional radius of curvature at said point of reflection. Itshould be understood that the image distance of said transmeridionalfocal line, u is a function of the meridional curvature and said angleof incidence i at said point of reflection.

In order to demonstrate the effects of eccentricity upon a theperipheral image size, and thereby demonstrate the method and apparatusof this invention, two examples will be used: (1) image formation andsize of said image of a given relatively large circular target at agiven object distance from a spherical reflecting surface of givenradius of curvature (FIG. 1), and (2.) image formation and size of saidimage of the same target and target distance from a paraboloidalreflecting surface having an apical radius of curvature equal to that ofthe sphere (FIG. 2).

FIG. 1, not drawn to scale, is used to represent the positions ofpoints, surfaces and chief rays involved in image formation byreflection from a spherical surface of an off-axis object point. Point Ois the object point, OP is the incident chief ray, and PE is thereflected chief ray, with point E being the center of the entrance pupilof the telescope. Line CE is the common optical axis of the telescopeand the spherical reflecting surface Q'AQ, whose center of curvature ispoint C. Line CK is the normal to the reflecting surface at point P, sothat angles OPK and K'PE are equal, and each equal to angle i previouslymentioned. Angle GB is 53.416 while angles OPK and IKPE are each 28.073.OC=CE=158 mm., while CA=CP =-8 mm. From the geometry of FIG. 1, andusing Equation 3, image distance PO, seen in the direction EP, iscalculated to be 3.448 mm., while image size X0 is calculated to be3.678 mm. Using two object points symmetrically placed with respect tooptical axis CE, the image size is then 7.356 mm. In this example, pointP is 3.594 mm. from the optical axis.

FIG. 2, not drawn to scale, is used to represent the positions ofpoints, surfaces and chief rays involved in image formation byreflection from a conicoid of revolution of an off-axis object point.Point O is the object point, OP is the incident chief ray and PE is thereflected chief ray, with point B being the center of the entrance pupilof the telescope. Line OE is the common optical axis of the telescopeand the conicoid reflecting surface Q'AQ, which in this example is aparaboloid. CA is the apical radius of curvature of the surface and is'8 mm. Line CK is the normal to the surface at point P, the medidionalradius of curvature C"'P at point P being 11.18 mm., while UP thetransmeridional radius of curvature at point P is 8.944 mm. Angle OOE is53.416" while angles OPK and KPE are each 28.082. In this example, pointP is 4 mm. from the optical axis. Distance CE=1.58 mm. While C'E=1.59mm. From the geometry of FIG. 2, and using :Equation 3, image distancePO, seen in the direction EP, is calculated to be 4.775 mm. Image sizeX0 is calculated to be 4.13 mm. Using two object points symmetricallyplaced with respect to the optical axis CE, the image size is then 8.26mm.

FIG. 3, drawn to exact scale, is used as a means of comparison of imagesizes and positions for the two images of FIGS. 1 and 2. Line ZZrepresents the combined optical axes of each of the two mirror surfaces,the spherical half mirror AQ being to the right of ZZ, and theparaboloidal half mirror AQ' being to the left of ZZ'. AX is the vertexdepth and X0 is the semidiameter of the image produced by the sphericalmirror, while AX is the vertex depth and X'O' is the semidiameter of theimage produced by the paraboloidal mirror. HP and HP represent thedistances of the points of reflection of the chief rays from the opticalaxes on the spherical and the paraboloidal mirrors respectively.

FIGS. 1, 2 and 3 demonstrate the marked difference in image size for thetwo surfaces having the same apical radius of curvature, 8 mm., butdifferent eccentricities, namely, 0 and 1, for the given large fixedsize object at the given object distance from the apex of the reflectingsurface. These size differences are readily measured by ophthalmometry,FIGS. 1, 2 and 3 further demonstrate that on the reflecting surface ofthe greater eccentricity, the point of reflection of the chief ray fromthe object point to the center of the entrance pupil of the telescope,is farther from the common optical axis of the reflecting surface andthe telescope. It is apparent that as the eccentricities of reflectingsurfaces of a given apical radius of curvature increase, the image sizeof a relatively large object will also increase. Thus, for a series ofconicoids of a given apical radius of curvature but of differenteccentricities, there will be a series of related image sizes for agiven relatively large target size, each image size corresponding to aparticular eccentricity.

In this invention, there are two separate and distinct targets on theapparatus: (1) a relatively small circular target of given diameter,concentric to the telescope optical axis in a given object plane, saidsmall target producing a small image by reflection, which image is usedfor the determination of the apical radius of curvature of thereflecting surface, all being considered to be under substantiallyparaxial conditions, and (2) a relatively large circular target ofifixed diameter, also concentric to the telescope optical axis, and in asecond object plane, object points in said two circular targets and thecenter of the entrance pupil of the telescope all being at substantiallyequal distances from a common point along said telescope optical axis.Said relatively large circular target produces a relatively large imageby reflection, whose size, when used in conjunction with the determinedapical radius of curvature of the reflecting surface, is used for thedetermination of the eccentricity of the reflecting surface, said secondtarget, the reflecting surface, the target image, and the telescopicobservation of said image, all being under nonparaxial conditions.

Although I have just stated that the targets are circles, they mayactually consist of a series of very small spots, small points of lightfor example, closely arrayed in a circular pattern, as previouslystated. Sharp focusing of the telescope upon the image produced byreflection is facilitated when the target consists of the small spots oflight. Further, with the use of said spots, the principal directions ofthe apex of the cornea can be readily determined when there is apicalastigmatism, by the directions of the focal lines of each spot, as thetelescope of the ophthalmometer is alternately focused upon each of thetwo sets of overlapping transmeridional focal lines, or upon each of thetwo sets of parallel meridional focal lines, while at the same timemeasuring the size of the transmeridional image as indicated by thesharply focused overlapping transmeridional lines for each of theprincipal directions. Similarly, with the large target composed of theseries of light spots arrayed in the circular pattern, each of the twoprincipal meridians and the size of the transmeridional image in each ofsaid meridians can be readily determined.

Since, for a cornea of a given apical radius of curvature, the measuredimage size of said relatively large target is a function of theeccentricity of said cornea, it is necessary that the apical radius ofcurvature and the size of the relatively large image of the given targetbe used in conjunction with each other for the determination of theeccentricity of said cornea. For example, one may tabulate a series ofcorneal apical radii of curvature, and then for each of said radii,there may be listed a series of image sizes for said relatively largetarget, each successively larger image size indicating a greatereccentricity of said cornea having said apical radius of curvature. Byreference to such a table, the two measurements of a cornea with the twosaid targets is sufficient for the determination of both the apicalradius of curvature and the eccentricity of said cornea. Instead oftabulating the data as just described, it may be presented graphically.It is to be understood that the dimensions of the apparatus, target sizeand target distance in particular, will affect the size of the cornealimage, and this is taken into account when constructing the apparatus.

In the examples given previously demonstrating the principles of thisinvention, which examples utilized FIGS. 1, 2 and 3, the actual valuesof target size and target distance for the larger of the two targets isa good example of the dimensions which are very adequate for carryingout this invention. Distances outward from the axis of the cornea, forthe points of reflection of the chief rays from target points, points Pof FIGS. 1 and 2, should be relatively large, from 3 to 5 mm. Theserelatively large distances makes possible significant differences inimage size for significant differences in eccentricities for corneas ofgiven specific apical radii of curvature. It should be understood thatconstructing the apparatus with somewhat different dimensions will onlyalter the range of image sizes for said larger target without departingfrom the basic method and apparatus of this invention. Regardless of thespecific dimensions which are used on the apparatus, the size of imagesproduced by a reflection of given size target at a given distance fromthe corneal apex of corneas having different apical radii of curvatureand different eccentricities, can be readily computed, utilizing mirrorequations, the law of reflection, and the geometry of conic sections,thus providing the data necessary for suitable tables or graphs.

A sample calculation showing the sequence of steps in the calculation ofimage size for a given relatively large target will be presented. Suchcalculation may be programmed for an electronic computer to obtain thedata for the tables or graphs previously referred to.

The sample calculation will be that for the surface illustrated insection in FIG. 2, a paraboloid having an apical radius of curvature r=CA, of 8 mm. Point P on the surface, 4 mm. from the optical axis ofsaid surface, has been selected as an appropriate distance laterally atwhich a chief ray from a target point 0 will be reflected to the centerof the entrance pupil E of the telescope.

The equation for a conicoid of revolution, including prolate ellipsoids,paraboloids, and hyperboloids of two sheets, which relate apical radiusof curvature r eccentricity, e, vertex depth, x, as measured along theaxis of said conicoid from its apex, and the distance, y, from saidaxis, of a point P(x,y) on said surface is:

Equation (4) may be solved by means of the quadratic formula, for valuesof x, for given values of e, r and y.

For the given example, where e=1, r =8 mm., and y=4 mm., the vertexdepth x of point P(x,y) is calculated by means of Equation (4) to be 1mm.

A normal through point P( 1,4), intersects the axis of the surface at C,at a distance from its apex equal to r +xe where xe =CC', so that C is 9mm. from said apex. The angle 7 which said normal makes with the axis ofthe surface at C is obtained by the following formula:

7 tan 1 (5) and is calculated to be 26.565 The distance OP is thetransmeridional radius of curvature rmns, of the surface at point P(1,4)and is calculated by means of the following formula:

trans TfY and for the example given is 8.944 mm.

The meridional radius of curvature at point P, r ,=C"P, can be obtainedfrom the values of rtrans. 'y, and e, by means of the followingequation:

y 1 a tan l50+x (s and a is calculated to be 1.517. The distancePE=y/sinu and is calculated to be 151.053 mm.

Angle i, the angle of reflection of the chief ray PE is equal to the sumof angles a and 'y, and is 28.082". By the law of reflection, angle i,the angle of incidence of the chief ray from the object point 0 to pointP on the surface, must also be 28.082".

To obtain sufiiciently large numerical values, the object point 0 was soselected that it lay in a plane perpendicular to the optical axis of thetelescope, said plane being at a distance of 86.168 mm. from the apex ofthe reflecting surface, with the object point 0 at a distance of 126.871mm. lateral to the common optical axes of the telescope and thereflecting surface.

By means of Pythagorean Theorum, and using the coordinates of points Pand 0, object distance OP=u is computed to be 150.650 mm.

Using object distance u=150.'650, r ,=11.180 mm., and i=28.082, andapplying these values to Equation (3), u'=PO' is calculated to be 4.775mm.

The distance of point 0' from the optical axis of the reflectingsurface, which is the image size X0, is calcu- 7 lated to be equal to Esin 0c, and is 4.13 mm. Assuming I. second object point at the samedistance on the oppo- ;ite side of the optical axis, therebyrepresenting two points out of a concentric circular target, the totalimage iize would 8.26 mm.

The essential feature characteristic of the above calcu- .ation is thecompliance with the law of reflection wherein .=i'. Hence for any givenlarge size target in a plane perpendicular to the common conicoidtelescope optical axis at a given distance from the apex of the conicoidre- Electing surface, having a given apical radius of curvature andeccentricity, the correct calculation of image size must show that i andi' are equal. If independently calculated values of i and i are unequal,this indicates an error has been made.

Suitable apparatus for carrying out this invention is indicated in FIG.4. A fixed housing has a cylindrical bore snugly fit to the telescope 21passing through the bore. The telescope is capable of rotation about itsopti- :al axis to any predetermined angular position where it is lockedin position at 22. Telescope 21 is prevented from longitudinal movementwithin the bore of housing 20 by means of a pin at the end of clamp 22which fits into a groove 23 of the telescope. A reticle 33 is fitted ineyepiece 48 and the reticle has two lines crossing at 90 and calibratedso as to read image sizes as will later be described. The angularposition of the telescope about its axis and the position of the reticle33 can be read on scale 24, fixed to housing 20, by means of pointer 25which is fixed to the telescope. One may thus adjust the reticle linesvertical and horizontal or, in the case of astigmatism, at other anglescorresponding to the principal meridians, as later described. Fixed tothe front end of the telescope is a bracket 26 which carries a smallercircular target 27 in the form of a circular fluorescent tube which isserved by a transformer and ballast indicated at 28 and which operatesin the usual manner. A second larger circular target 29 is also mountedon bracket 26 and is in the form shown here of a circular fluorescenttube served by the usual transformer and ballast 30. The targets 27 and29 are concentric about the optical axis of the telescope 21.

Housing 20 is rigidly mounted by post 34 to the base 35 and is capableof motion in three directions, one vertical and two horizontal. One ofthe horizontal motions is in a direction parallel to the axis of thetelescope and involves slides 36 slidable on ways carried by cross slide38. The slide adjustment at 36 is controlled by knob 37. The secondhorizontal motion is in a direction perpendicular to the telescope axisand involves slide 38 mounted on base 35 and controlled by screw 39. Thevertical motion involves a worm and screw arrangement 40 controlled byknob 41.

The telescopic apparatus is mounted on a table 42 which also carries apedestal 43 upon which is adjustably mounted a chin rest 44 adjustableby means shown at 45. A forehead rest 46 is supported on pedestal 43above the chin rest 44. From the head rest extends an occluder 47 whichcan be oscillated in front of either eye. The position of the patientseye is indicated at 48 and it should be understood that if a lens isbeing examined it is suitably supported in the position 48.

Using the dimensions of FIGS. 1 and 2, the telescope is so focused thatwhen the object plane is about 154 mm. from the telescope objectivelens, the image plane is at the reticle of the telescope eyepiece whensaid eyepiece is set at the zero position. For a cornea having an apicalradius of curvature of about 8 mm., the small circular target and saidtelescope objective lens will be at about 150 mm. from the apex of thecornea and the corneal image of said target will be virtual and about 4mm. behind the corneal apex.

In the performance of ophthalmometry for the determination of the apicalradius of curvature of the cornea, the telescope is sharply focused uponthe corneal image by moving said telescope toward or away from saidimage. Hence the object distance varies slightly as a function of theapical radius of curvature of the cornea since the small circular targetis fixed to the telescope. Once the object distance has been fixed byfocusing the telescope upon the image of said small circular target, theobject distance for the large circular target is likewise fixed. Sharpfocusing of the telescope upon said corneal image is then accomplishedby means of adjustment of the telescope eyepiece. This is a preferredmethod of focusing upon said corneal image.

There will now be outlined in a series of steps the procedure fordetermining the apical radius of curvature and eccentricity of a corneaby the method and apparatus of this invention.

1. The patient is seated at the apparatus of FIG. 4 with the head leveland held firmly in position by means of head rest 46 and chin rest 44,the height of the chin rest being adjusted to bring the level of theeyes approximately the same height as the optical axis of telescope 21.

2. Occluder 47 is adjusted to obstruct vision of the left eye.

3. The patient is asked to direct his gaze to the center of thetelescope tube which he faces.

4. Telescope eyepiece 48 is set at zero position by knob 49 and thetelescope is rotated about its optical axis setting pointer 25 at zeroon scale 24, which positions the cross lines of reticle 33 horizontaland vertical respectively.

5. Small circular target 27 is illuminated, and by means of adjustingscrews 37, 39 and 41, the corneal image of target 27 is sharply focusedand centered about the crosshairs of the reticle 33 as seen through thetelescope eyepiece 48.

6. The size of said circular image is measured directly on the reticleand said measurement is used in association with a table to indicate theapical radius of curvature of the cornea.

7. Illumination of the small circular target is discontinued and thelarge circular target 29 is then illuminated. By means of knob 49telescope eyepiece 48 is adjusted until the corneal image of saidtargetas seen through the telescope is sharply focused on the reticle at48 and its size is measured on reticle 33. Reference is then made to thegraphs or tables which relate apical radius of curvature of the corneaand image size of the large circular target, thereby obtaining theeccentricity of the cornea measured.

8. When the cornea is astigmatic at its apex, the procedure as outlinedin the seven previous steps is performed for each of the two principalmeridians of the cornea.

9. The occluder 47 is then adjusted to obstruct vision of the right eye,and steps (1) through (b)8 repeated.

The line of sight of the eye is generally directed about 5 nasal to theaxis of the cornea, intersecting the cornea about .5 mm. nasal to theapex of the cornea. Consequently the image of the target, thoughcentered about the optical axis of the telescope, may not be centeredwith respect to the optical axis of the cornea. If more prec-ise resultsare desired, the angular separation of the line of sight of the eye andthe optical axis of the cornea may be determined, by methods known inthe art, and this angle taken into account when measuring the cornea.For this purpose I provide a supplementary fixation target (not shown)which can be moved with respect to the optical axis of the telescope,and thereby cause the corneal axis and the optical axis of the telescopeto approximately coincide.

The major advantage of this invention, method and apparatus, fordetermining the two parameters, apical radius of curvature andeccentricity, which fully describe a conicoid of revolution, includingthe cornea which can be related to a conicoid, is that the previouslyknown procedure requiring relative rotation of the measured surface isdone away with. Instead, the present invention requires only a singlealinement of the cornea, or conicoid, and the optical axis of theinstrument; thereafter requiring only clear focusing of the image tomeasure the apical radius of curvature and eccentricity of the cornea,and possibly telescope adjustment for measurement in one or moreprincipal meridians. Furthermore, the measurements which are made forany given meridian involve both halves of the cornea simultaneously,since the image of said targets is substantially symmetrical about thecorneal axis, either in the case where the cornea is substantially asurface of revolution, or in the case where the cornea is not a surfaceof revolution, but instead has two principal meridians. Further, inthose instances of corneal asymmetry, the simultaneous involvement ofopposite halves of the cornea in image formation, has the effect ofyielding measurements which are an approximate average for the meridiansmeasured.

Although in the description so far I have shown the targets to be twoseparate targets, there may in fact be only one large concave sphericalbowl-shaped target which is masked first to yield a small circularlyoutlined illuminated area serving for the measurement of the apicalradius of curvature of the cornea, and then masked to yield a largecircularly outlined illuminated area to serve as the second target, withthe border of each of the areas representing the target points. Inanother form or embodiment of the apparatus of this invention, eachtarget may be a separate circular illuminated area, either a continuouscircle or a series of spots arrayed circularly. Although I havedescribed that the targets be illuminated succesively in the outline ofthe procedure for using the method and apparatus of this invention, bothtargets may be illuminated simultaneously without alfecting the results.

Regardless of the type of target, or whether one or both targets areilluminated at the same time, the principles outlined in the inventionremain the same.

For the measurement of apical radius of curvature and eccentricity ofcontact lenses the procedure is the same as outlined for the measurementof the cornea. For the measurement of convex conicoid surfaces,theapical radius of curvature determined by the image size, and the sizeof the image of the large target, have the same relationship as they dofor the measurement of the cornea. For the concave conicoids ofrevolution, the images of the two targets are both slightly smaller thanthose for the convex surfaces of the same apical radius of curvature andeccentricity. Consequently the data provided in tabular form, orgraphically, for the concave surface is slightly different than thatprovided for the convex surface.

For the purposes of this invention, the targets 27 and 29 need. not liein different planes as indicated in FIG. 4, but this arrangement wasselected as a more convenient form of apparatus, and as a means ofsimplifying the calculations.

Wherever in the specification and claims I have referred to measuringthe size of an image on the reticle of the telescope, I intend toinclude the use of supplementary adjustable doubling systems in thetelescope for measuring image size, such equivalents being well known inthe art.

I claim:

1. The method of determining the apical radius of curvature, r, and theeccentricity, e, of [a] an optical conicoid surface and :[or in each ofthe principal meridians] of a reflecting surface such as a cornea whoseprincipal sections are conics in each of the principal meridians, byobserving through a telescope having a reticle with two lines crossingat 90 degrees on the optical axis of said telescope, [at least one ofsaid cross lines calibrated and marked for image size measurement,] twoimages of two distinct circular targets as represented by at least twodistinct points for each of said targets at opposite ends of [adiameter] diameters thereof along a principal meridian of the corneareflecting said [image] images, one of said targets relatively small andthe other relatively large, and one of said images relatively small andthe other relatively large, comprising the steps of (1) supporting saidtwo circular targets concentric to the optical axis of said telescopeand normal to said axis; (2) observing through said telescope andmanually focusing upon the image of the smaller of said two targetsformed by said reflecting surface [surfaces]; (3) adjusting the positionof said reflecting surface so that its optical axis is alined with theoptical axis of said telescope whereby the image of said small circulartarget is centered upon the crossing point of said reticle; (4) when thesmall image is generally elliptical, as in the case of apicalastigmatism of the reflecting surface, rotating said telescope about itsoptical axis so that the cross lines of said reticle coincide in adirection with the major and minor axes of the generally ellipticalrelatively small image; (5) manually sharply focusing upon and measuringthe size of said image [on said reticle] for each of the two principalmeridians [and relating said sizes to the apical radii of curvature foreach of said meridians of said surface]; (6) when the small image iscircular, as in the case where there is no apical astigmatism of thereflecting surface, manually sharply focusing upon and measuring thesize of said image [on said reticle and relating said size to the apicalradius of curvature of said surface]; (7) observing through saidtelescope and manually focusing upon the image of the larger of said twotargets formed by said reflecting surface; (8) when the large image isgenerally elliptical, rotating said telescope about its optical axis sothat the cross lines of said reticle coincide in a direction with themajor and minor axes of said generally elliptical relatively largeimage; (9) manually sharply focusing upon and measuring the size of saidimage [on said reticle] for each of the said two principal directions;(10) when the large image is circular, measuring the size of saidcircular image [on said reticle; relating the apical radii of curvatureof said surface and the image size of the large target for each of thetwo principal directions of said surface to the eccentricity of saidsurface in each of said two principal directions]; (11) relating saidsmall and large image sizes for each of said principal meridians to theapical radius of curvature and eccentricity in each of said principalmeridians; and (12) when said small and large images are both circular,relating said small and large image sizes to the apical radius ofcurvature and eccentricity of said surface which is a conicoid.

References Cited The following references, cited by the Examiner, are ofrecord in the patented file of this patent or the original patent.

UNITED STATES PATENTS 1,918,540 7/1933 Hartinger 351l3 2,482,669 "9/1949 Harding 35 l23 3,248,162 4/ 1966 Knoll 35113 X 3,264,932 8/1966:Hendricks 351-40 X FOREIGN PATENTS 11,409 3/1906 Great Britain 3516OTHER REFERENCES Henry A. Knoll: Corneal Contours-Revealed by thePhotokeratoscope, Amer. J. Optom. & Archives of Amer. Acad. Optom., pp.389-397, vol. 38, July 7, 1961.

DAVID SCHONBERG, 'Primary Examiner P. A. SACHER, Assistant Examiner US.Cl. X.R. 351- 6, 13, 16, 40

